If painting exclusively with Tamiya acrylics, water will suffice for the initial rinse-out of any leftovers in the paint cup, but I would follow that by spraying denatured alcohol or Windex through the brush until no trace of paint comes through. (If using Windex, follow with distilled water to prevent the ammonia in the Windex from attacking the metal in the airbrush and/or contaminating the next colour you put through the airbrush) If you're just switching colours, this should be sufficient.
When finished painting for the day, repeat the above and then unscrew the tip and swab out the tip with a cloth dampened with alcohol. Withdraw the needle and wipe down with a cloth dampened with alcohol. Be very careful not to damage the tip of the needle. Reassemble and you are good to go.
Regarding thinning Tamiya acrylics, it has been said that a small amount of water works, though I've never tried it. Personally, I wouldn't use water, as I believe too much water tends to (a)alter the surface tension of the paint and (b) reduces the effectiveness of the "binder" in the paint, resulting in poor adhesion.
My personal preference is to use denatured alcohol to thin Tamiya acrylics, plus a drop of acrylic retarder, which helps to prevent "tip dry".